Peptide crystal simulations reveal hidden dynamics

Abstract

Molecular dynamics simulations of biomolecular crystals at atomic resolution have the potential to recover information on dynamics and heterogeneity hidden in X-ray diffraction data. We present here 9.6 μs of dynamics in a small helical peptide crystal with 36 independent copies of the unit cell. The average simulation structure agrees with experiment to within 0.28 Å backbone and 0.42 Å all-atom RMSD; a model refined against the average simulation density agrees with the experimental structure to within 0.20 Å backbone and 0.33 Å all-atom RMSD. The R-factor between the experimental structure factors and those derived from this unrestrained simulation is 23% to 1.0 Å resolution. The B-factors for most heavy atoms agree well with experiment (Pearson correlation of 0.90), but B-factors obtained by refinement against the average simulation density underestimate the coordinate fluctuations in the underlying simulation where the simulation samples alternate conformations. A dynamic flow of water molecules through channels within the crystal lattice is observed, yet the average water density is in remarkable agreement with experiment. A minor population of unit cells is characterized by reduced water content, 310 helical propensity and a gauche(-) side-chain rotamer for one of the valine residues. Careful examination of the experimental data suggests that transitions of the helices are a simulation artifact, although there is indeed evidence for alternate valine conformers and variable water content. This study highlights the potential for crystal simulations to detect dynamics and heterogeneity in experimental diffraction data as well as to validate computational chemistry methods.

Figure 1

Three views of the simulated fav8 crystal lattice. 36 unit cells are stacked in a 4 × 3 × 3 arrangement in the triclinic super-system; each unit cell comprises two fav8 decapeptide helices arranged roughly parallel to one another. Each view looks down one axis of the lattice; borders of the simulated system are marked in black lines. The peptide backbone is shown in ribbons, or in licorice form in the case of Aib and terminal blocking residues. Water molecules are illustrated in space-filling form; we find that the water forms continuous channels running through the lattice along the a axis.

Figure 2

Positional RMSDs of heavy atoms relative to the X-ray structure. Details of each metric are given in the main text; all quantities are plotted over the course of a 2.4 μs simulation, and plots for three additional 1.6 μs simulations are given in the supporting information. Purple: ASU RMSD for backbone (N,CA,C) atoms. Orange: ASU RMSD for side-chain heavy atoms. Blue: lattice RMSD for backbone atoms.

Figure 3

Superposition of the average simulated structure (black) against the structure refined from diffraction data (orange). The first decapeptide (monomer A) matches the X-ray data closely; monomer B deviates in the side-chain conformation of its Val residue and in the helicity of its C-terminal backbone residues 16–20.

Figure 4

Volume of the supercell over the course of a 2.4 μs simulation. Following an initial settling, the system volume reaches an equilibrium value roughly 0.2% below the volume of the unit cell observed by X-ray diffraction. Instantaneous fluctuations of the volume have amplitudes of an additional 0.2%.

Figure 5

Left-hand plot: Comparison of computed atomic B-factors obtained over the course of the 2.4 μs trajectory to experimental data. “RMSD” B-factors only account for intra-ASU fluctuations and consistently underestimate experimental values. “Reverse symmetry” B-factors account for both local and global (inter-ASU) fluctuations and more closely match experiment. See text for further explanation of the two methods. Right-hand plot: Comparison of B-factors obtained from refinement against the experimental density and against the simulation average density. Backbone atoms are indicated with dots.

Figure 6

Mean square displacements (msd) of water molecules over the course of three 1.6 μs and one 2.4 μs simulation trajectories. The slope of the linear fit used to compute the diffusion coefficient is shown in box.

Figure 7

Water densities in the channels observed in simulations. The left-hand panel depicts the density of waters as a function of the a crystal vector coordinate, summed over all nine channels running across the simulation box. The abscissa is numbered according to unit cell fractional coordinates. The right-hand panel plots a histogram of times which each unit cell in the simulation was observed to be associated with a particular number of waters during the 2.4 μs trajectory.

Figure 8

Water density observed in the 2.4 μs simulation, obtained by using crystal symmetry operations to superimpose all simulated waters onto a single unit cell. Crystallographic peptide is shown in orange/yellow and crystallographic water oxygens as red spheres. Left-hand panel shows the simulated water density (mesh encloses 90% of water density), right-hand panel shows the electron density obtained by X-ray diffraction (2mFo-DFcalc map at 0.8 sigma). Green arrows point to crystallographic waters and indicate their experimental B-factors, purple arrow shows a fifth lobe of water density (see text). Produced with VMD and ccp4mg.

Figure 9

Mean residence times for each occurring water state over the course of the 2.4 μs trajectory. The one and two water states, though much less frequent than other states (cf. Figure 7), exhibit very long residence times, in some cases extending into hundreds of nanoseconds.

Figure 10

Correlation, as a function of measurement time, between the presence of a Val B8 gauche(−) rotamer, 1- or 2-water defects, and 3₁₀ helical conformation. A conformational change of monomer B helicity is found to be more strongly connected to water defects than either condition is to the Val B8 rotamer state.

Figure 11

Experimental electron density of the Valine B8 side chain reveals evidence for partial occupancy of the trans rotamer that is preferentially sampled in our simulations. The left-hand panel shows the Fo-Fc map sampled on a 0.50 Å3 grid and contoured at 4.0 (green) and −4.0 (red) in the vicinity of valine B8 (purple). The valine side chain is seen in the experimentally determined gauche(−) rotamer. A region of positive density indicates the missing alternate trans rotamer sampled in our simulation. Image generated with ccp4mg. The right-hand panel shows the output of Ringer for the χ₁ angle of valine A8 (black) and B8 (blue). An additional peak in the latter case points to the presence of a partially occupied trans rotamer in the electron density.